The book discusses hidden symmetries in the Anti-de Sitter/conformal field theory (AdS/CFT) duality. This duality is a modern concept that asserts an exact duality between conformally invariant quantum field theories and string theories in higher dimensional Anti-de Sitter spaces, and in this way provides a completely new tool for the study of strongly coupled quantum field theories. In this setting, the book focuses on the Wilson loop, an important observable in four-dimensional maximally supersymmetric gauge theory. The dual string description using minimal surfaces enables a systematic study of the hidden symmetries of the loop. The book presents major findings, including the discovery of a master symmetry for strings in general symmetric spaces, its relation to the Yangian symmetry algebra and its action on the minimal surfaces appearing in the dual string description of the Wilson loop. Moreover, it clarifies why certain symmetries are not present on the gauge theory side for purely bosonic Wilson loops and, lastly, how the supersymmetrization of the minimal surface problem for type IIB superstrings can be undertaken. As such, it substantially increases our understanding and use of infinite dimensional symmetries occurring in the AdS/CFT correspondence.

This book provides an itinerary to quantum mechanics taking into account the basic mathematics to formulate it. Specifically, it features the main experiments and postulates of quantum mechanics pointing out their mathematical prominent aspects showing how physical concepts and mathematical tools are deeply intertwined. The material covers topics such as analytic mechanics in Newtonian, Lagrangian, and Hamiltonian formulations, theory of light as formulated in special relativity, and then why quantum mechanics is necessary to explain experiments like the double-split, atomic spectra, and photoelectric effect. The Schroedinger equation and its solutions are developed in detail. It is pointed out that, starting from the concept of the harmonic oscillator, it is possible to develop advanced quantum mechanics. Furthermore, the mathematics behind the Heisenberg uncertainty principle is constructed towards advanced quantum mechanical principles. Relativistic quantum mechanics is finally considered.The book is devoted to undergraduate students from University courses of Physics, Mathematics, Chemistry, and Engineering. It consists of 50 self-contained lectures, and any statement and theorem are demonstrated in detail. It is the companion book of "A Mathematical Journey to Relativity", by the same Authors, published by Springer in 2020.

Intended for beginning graduate students, this text takes the reader from the familiar coordinate representation of quantum mechanics to the modern algebraic approach, emphasizing symmetry principles throughout. After an introduction to the basic postulates and techniques, the book discusses time-independent perturbation theory, angular momentum, identical particles, scatteering theory, and time-dependent perturbation theory. The whole is rounded off with several lectures on relativistic quantum mechanics and on many-body theory.

This thesis describes the first demonstration of a cooperative optical non-linearity based on Rydberg excitation. Whereas in conventional non-linear optics the non-linearity arises directly from the interaction between light and matter, in a cooperative process it is mediated by dipole-dipole interactions between light-induced excitations. For excitation to high Rydberg states where the electron is only weakly bound, the dipole-dipole interactions are extremely large and long range, enabling an enormous enhancement of the non-linear effect. Consequently, cooperative non-linear optics using Rydberg excitations opens a new era for quantum optics enabling large single photon non-linearity to be accessible in free space for the first time. The thesis describes the theoretical underpinnings of the non- linear effect, the pioneering experimental results and implications for experiments in the single photon regime.

This book discusses particle physics and relativistic local field theory that is the main theoretical tool for analyzing particle physics. It is helpful for the professional physicist and to the serious graduate student of physics.

This book contains contributions written by the world-leading scientists in high-resolution laser spectroscopy, quantum optics and laser physics. Emphasis is placed on precision related to results in a variety of fields, such as atomic clocks, frequency standards, and the measurement of physical constants in atomic physics. Furthermore, illustrations and engineering applications of the fundamentals of quantum mechanics are widely covered. It has contributions by Nobel prize winners Norman F. Ramsey and Steven Chu, and is dedicated to Theodor W. Hänsch on the occasion of his 60th birthday.

Offers a whistle-stop tour through the early part of the 20th century when the founding fathers of quantum theory forever altered the frontiers of human thought Provides an example-filled interpretation of the theory, its applications, and its pinnacle in quantum field theory (QFT), so crucial in shaping ideas about the nature of reality Separates fact from speculation regarding quantum physics' ability to provide a starting point for philosophical queries into ultimate understanding and the limits of science

Quantum theory is at the foundation of the physical description of our world. One of the people who contributed significantly to our conceptual understanding of this theory was Heinz-Dieter Zeh (1932-2018). He was the pioneer of the process of decoherence, through which the classical appearance of our world can be understood. This volume presents a collection of essays dedicated to his memory, written by distinguished scientists and scholars. They cover all aspects of the interpretation of quantum theory in general and the quantum-to-classical transition in particular. This volume provides illuminating reading to anyone seeking a deep understanding of quantum theory and its relevance to the foundations of physics.

This book introduces the fundamentals of the theory of quantum computing, illustrated with code samples written in Q#, a quantum-specific programming language, and its related Quantum Development Kit. Quantum computing (QC) is a multidisciplinary field that sits at the intersection of quantum physics, quantum information theory, computer science and mathematics, and which may revolutionize the world of computing and software engineering. The book begins by covering historical aspects of quantum theory and quantum computing, as well as offers a gentle, algebra-based, introduction to quantum mechanics, specifically focusing on concepts essential for the field of quantum programming. Quantum state description, state evolution, quantum measurement and the Bell's theorem are among the topics covered. The readers also get a tour of the features of Q# and familiarize themselves with the QDK. Next, the core QC topics are discussed, complete with the necessary mathematical formalism. This includes the notions of qubit, quantum gates and quantum circuits. In addition to that, the book provides a detailed treatment of a series of important concepts from quantum information theory, in particular entanglement and the no-cloning theorem, followed by discussion about quantum key distribution and its various protocols. Finally, the canon of most important QC algorithms and algorithmic techniques is covered in-depth - from the Deutsch-Jozsa algorithm, through Grover's search, to Quantum Fourier Transform, quantum phase estimation and Shor's algorithm. The book is an accessible introduction into the vibrant and fascinating field of quantum computing, offering a blend of academic diligence with pragmatism that is so central to software development world. All of the discussed theoretical aspects of QC are accompanied by runnable code examples, providing the reader with two different angles - mathematical and programmatic - of looking at the same problem space.

A spectacular musical and scientific journey from the Bronx to the cosmic horizon that reveals the astonishing links between jazz, science, Einstein, and Coltrane More than fifty years ago, John Coltrane drew the twelve musical notes in a circle and connected them by straight lines, forming a five-pointed star. Inspired by Einstein, Coltrane put physics and geometry at the core of his music. Physicist and jazz musician Stephon Alexander follows suit, using jazz to answer physics' most vexing questions about the past and future of the universe. Following the great minds that first drew the links between music and physics-a list including Pythagoras, Kepler, Newton, Einstein, and Rakim -- The Jazz of Physics reveals that the ancient poetic idea of the "Music of the Spheres," taken seriously, clarifies confounding issues in physics. The Jazz of Physics will fascinate and inspire anyone interested in the mysteries of our universe, music, and life itself.

This book bridges a gap between two major communities of Condensed Matter Physics, Semiconductors and Superconductors, that have thrived independently. Through an original perspective that their key particles, excitons and Cooper pairs, are composite bosons, the authors raise fundamental questions of current interest: how does the Pauli exclusion principle wield its power on the fermionic components of bosonic particles at a microscopic level and how this affects the macroscopic physics? What can we learn from Wannier and Frenkel excitons and from Cooper pairs that helps us understand "bosonic condensation" of composite bosons and its difference from Bose-Einstein condensation of elementary bosons? The authors start from solid mathematical and physical foundation to derive excitons and Cooper pairs. They further introduce Shiva diagrams as a graphic support to grasp the many-body physics induced by fermion exchange - a novel mechanism not visualized by standard Feynman diagrams. Advanced undergraduate or graduate students in physics with no prior background will benefit from this book. The developed concepts and methodology should also be useful to present researches on ultracold atomic gases, exciton-polaritons, and quantum information.

Niels Bohr (1885-1962) was a Danish physicist who played a key role in the development of atomic theory and quantum mechanics, he was awarded the Nobel Prize for Physics in 1922. First published in 1924, this concise volume provides an English translation of a 1923 German language essay which appeared in the Zeitschrift fur Physik journal. It concerns itself with the fundamental postulates of quantum theory, aiming to present the principles of the theory in such a way that their application appears free from contradiction. This book will be of value to anyone with an interest in Bohr's contribution to physics.

This volume presents detailed discussions of a number of unsolved conceptual and technical issues arising, in particular, in the foundations of quantum theory and the philosophy of science. The 14 contributions capture a wide variety of viewpoints and backgrounds. Some chapters deal primarily with the main experimental issues; others focus on theoretical and philosophical questions. In addition, attempts are made to systematically analyze ways in which quantum physics can be connected to the neurosciences and consciousness research.

This textbook is a unique and ambitious primer of nuclear physics, which introduces recent theoretical and experimental progresses starting from basics in fundamental quantum mechanics. The highlight is to offer an overview of nuclear structure phenomena relevant to recent key findings such as unstable halo nuclei, superheavy elements, neutron stars, nucleosynthesis, the standard model, lattice quantum chromodynamics (LQCD), and chiral effective theory. An additional attraction is that general properties of nuclei are comprehensively explained from both the theoretical and experimental viewpoints. The book begins with the conceptual and mathematical basics of quantum mechanics, and goes into the main point of nuclear physics - nuclear structure, radioactive ion beam physics, and nuclear reactions. The last chapters devote interdisciplinary topics in association with astrophysics and particle physics. A number of illustrations and exercises with complete solutions are given. Each chapter is comprehensively written starting from fundamentals to gradually reach modern aspects of nuclear physics with the objective to provide an effective description of the cutting edge in the field.

This monograph draws on two traditions: the algebraic formulation of quantum mechanics as well as quantum field theory, and the geometric theory of classical mechanics. These are combined in a unified treatment of the theory of Poisson algebras of observables and pure state spaces with a transition probability, which leads on to a discussion of the theory of quantization and the classical limit from this perspective. A prototype of quantization comes from the analogy between the C*- algebra of a Lie groupoid and the Poisson algebra of the corresponding Lie algebroid. The parallel between reduction of symplectic manifolds in classical mechanics and induced representations of groups and C*- algebras in quantum mechanics plays an equally important role. Examples from physics include constrained quantization, curved spaces, magnetic monopoles, gauge theories, massless particles, and $theta$- vacua. Accessible to mathematicians with some prior knowledge of classical and quantum mechanics, and to mathematical physicists and theoretical physicists with some background in functional analysis.

This open access monograph offers a detailed study and a systematic defense of a key intuition we typically have, as human beings, with respect to the nature of time: the intuition that the future is open, whereas the past is fixed. For example, whereas it seems unsettled whether there will be a fourth world war, it is settled that there was a first world war. The book contributes, in particular, three major and original insights. First, it provides a coherent, non-metaphorical, and metaphysically illuminating elucidation of the intuition. Second, it determines which model of the temporal structure of the world is most appropriate to accommodate the intuition, and settles on a specific version of the Growing Block Theory of time (GBT). Third, it puts forward a naturalistic foundation for GBT, by exploiting recent results of our best physics (viz. General Relativity, Quantum Mechanics, and Quantum Gravity). Three main challenges are addressed: the dismissal of temporal asymmetries as non-fundamental phenomena only (e.g., thermodynamic or causal phenomena), the epistemic objection against GBT, and the apparent tension between GBT and relativistic physics. It is argued that the asymmetry between the open future and the fixed past must be grounded in the temporal structure of the world, and that this is neither precluded by our epistemic device, nor by the latest approaches to Quantum Gravity ( e.g., the Causal Set Theory). Aiming at reconciling time as we find it in ordinary experience and time as physics describes it, this innovative book will raise the interest of both academic researchers and graduate students working on the philosophy of time. More generally, it presents contents of interest for all metaphysicians and non-dogmatic philosophers of physics. This is an open access book.

This book is aimed at providing a coherent, essentially self-contained, rigorous and comprehensive abstract theory of Feynman's operational calculus for noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and time-ordering rules in his seminal 1951 paper An operator calculus having applications in quantum electrodynamics, as will be made abundantly clear in the introduction (Chapter 1) and elsewhere in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work. Hence, the second part of the main title of this book. The basic properties of the operational calculus are developed and certain algebraic and analytic properties of the operational calculus are explored. Also, the operational calculus will be seen to possess some pleasant stability properties. Furthermore, an evolution equation and a generalized integral equation obeyed by the operational calculus are discussed and connections with certain analytic Feynman integrals are noted. This volume is essentially self-contained and we only assume that the reader has a reasonable, graduate level, background in analysis, measure theory and functional analysis or operator theory. Much of the necessary remaining background is supplied in the text itself.

Relative entropy has played a significant role in various fields of mathematics and physics as the quantum version of the Kullback-Leibler divergence in classical theory. Many variations of relative entropy have been introduced so far with applications to quantum information and related subjects. Typical examples are three different classes, called the standard, the maximal, and the measured f-divergences, all of which are defined in terms of (operator) convex functions f on (0, ) and have respective mathematical and information theoretical backgrounds. The -Renyi relative entropy and its new version called the sandwiched -Renyi relative entropy have also been useful in recent developments of quantum information. In the first half of this monograph, the different types of quantum f-divergences and the Renyi-type divergences mentioned above in the general von Neumann algebra setting are presented for study. While quantum information has been developing mostly in the finite-dimensional setting, it is widely believed that von Neumann algebras provide the most suitable framework in studying quantum information and related subjects. Thus, the advance of quantum divergences in von Neumann algebras will be beneficial for further development of quantum information. Quantum divergences are functions of two states (or more generally, two positive linear functionals) on a quantum system and measure the difference between the two states. They are often utilized to address such problems as state discrimination, error correction, and reversibility of quantum operations. In the second half of the monograph, the reversibility/sufficiency theory for quantum operations (quantum channels) between von Neumann algebras via quantum f-divergences is explained, thus extending and strengthening Petz' previous work. For the convenience of the reader, an appendix including concise accounts of von Neumann algebras is provided.

Scattering amplitudes are fundamental and rich observables in quantum field theory. Based on the observation that, for massless particles of spin-one or more, scattering amplitudes are much simpler than expected from traditional Feynman diagram techniques, the broad aim of this work is to understand and exploit this hidden structure. It uses methods from twistor theory to provide new insights into the correspondence between scattering amplitudes in supersymmetric Yang-Mills theory and null polygonal Wilson loops. By additionally exploiting the symmetries of the problem, the author succeeds in developing new ways of computing scattering amplitudes.

This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the anti-self-dual Yang-Mills equation in four dimensions. In the first part of the book, starting with the systematic description of the instanton, how to integrate out the instanton moduli space is explained together with the equivariant localization formula. It is then illustrated that this formalism is generalized to various situations, including quiver and fractional quiver gauge theory, supergroup gauge theory. The second part of the book is devoted to the algebraic geometric description of supersymmetric gauge theory, known as the Seiberg-Witten theory, together with string/M-theory point of view. Based on its relation to integrable systems, how to quantize such a geometric structure via the -deformation of gauge theory is addressed. The third part of the book focuses on the quantum algebraic structure of supersymmetric gauge theory. After introducing the free field realization of gauge theory, the underlying infinite dimensional algebraic structure is discussed with emphasis on the connection with representation theory of quiver, which leads to the notion of quiver W-algebra. It is then clarified that such a gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of W-algebra.

In this book, H. S. Green, a former student of Max Born and well known as an author in physics and in philosophy of science, presents an individual and modern approach to theoretical physics and related fundamental problems. Starting from first principles, the links between physics and information science are unveiled step by step: modern information theory and the classical theory of the Turing machine are combined to create a new interpretation of quantum computability, which is then applied to field theory, gravitation and submicroscopic measurement theory and culminates in a detailed examination of the role of the conscious observer in physical measurements. The result is a highly readable book that unifies a wide range of scientific knowledge and is essential reading for all scientists and philosophers of science interested in the interpretation and the implications of the interaction between information science and basic physical theories.

Quantum groups have been studied intensively in mathematics and have found many valuable applications in theoretical and mathematical physics since their discovery in the mid-1980s. Roughly speaking, there are two prototype examples of quantum groups, denoted by Uq and Aq. The former is a deformation of the universal enveloping algebra of a Kac-Moody Lie algebra, whereas the latter is a deformation of the coordinate ring of a Lie group. Although they are dual to each other in principle, most of the applications so far are based on Uq, and the main targets are solvable lattice models in 2-dimensions or quantum field theories in 1+1 dimensions. This book aims to present a unique approach to 3-dimensional integrability based on Aq. It starts from the tetrahedron equation, a 3-dimensional analogue of the Yang-Baxter equation, and its solution due to work by Kapranov-Voevodsky (1994). Then, it guides readers to its variety of generalizations, relations to quantum groups, and applications. They include a connection to the Poincare-Birkhoff-Witt basis of a unipotent part of Uq, reductions to the solutions of the Yang-Baxter equation, reflection equation, G2 reflection equation, matrix product constructions of quantum R matrices and reflection K matrices, stationary measures of multi-species simple-exclusion processes, etc. These contents of the book are quite distinct from conventional approaches and will stimulate and enrich the theories of quantum groups and integrable systems.

Quantum dots are nanometer-size semiconductor structures, and represent one of the most rapidly developing areas of current semiconductor research as increases in the speed and decreases in the size of semiconductor devices become more important. They present the utmost challenge to semiconductor technology, making possible fascinating novel devices. This important new reference book focuses on the key phenomena and principles. Chapter 1 provides a brief account of the history of quantum dots, whilst the second chapter surveys the various fabrication techniques used in the past two decades, and introduces the concept of self-organized growth. This topic is expanded in the following chapter, which presents a broad review of self-organization phenomena at surfaces of crystals. Experimental results on growth of quantum dot structures in many different systems and on their structural characterization are presented in Chapter 4. Basic properties of the dots relate to their geometric structure and chemical composition. Numerical modeling of the electronic and optical properties of real dots is presented in Chapter 5, together with general theoretical considerations on carrier capture, relaxation, recombination and properties of quantum dot lasers. Chapters 6 and 7 summarize experimental results on electronic, optical and electrical properties. The book concludes by disoussing highly topical results on quantum-dot-based photonic devices — mainly quantum dot lasers. Quantum Dot Heterostructures is written by some of the key researchers who have contributed significantly to the development of the field, and have pioneered both the theoretical understanding of quantum dot related phenomena and quantum dot lasers. It is of great interest to graduate and postgraduate students, and to researchers in semiconductor physics and technology and optoelectronics.

In this thesis, the first measurement of the running of the top quark mass is presented. This is a fundamental quantum effect that had never been studied before. Any deviation from the expected behaviour can be interpreted as a hint of the presence of physics beyond the Standard Model. All relevant aspects of the analysis are extensively described and documented. This thesis also describes a simultaneous measurement of the inclusive top quark-antiquark production cross section and the top quark mass in the simulation. The measured cross section is also used to precisely determine the values of the top quark mass and the strong coupling constant by comparing to state-of-the-art theoretical predictions. All the theoretical and experimental aspects relevant to the results presented in this thesis are discussed in the initial chapters in a concise but complete way, which makes the material accessible to a wider audience.

This book presents quantum theory as a theory based on new relationships among matter, thought, and experimental technology, as against those previously found in physics, relationships that also redefine those between mathematics and physics in quantum theory. The argument of the book is based on its title concept, reality without realism (RWR), and in the corresponding view, the RWR view, of quantum theory. The book considers, from this perspective, the thinking of Bohr, Heisenberg, Schroedinger, and Dirac, with the aim of bringing together the philosophy and history of quantum theory. With quantum theory, the book argues, the architecture of thought in theoretical physics was radically changed by the irreducible role of experimental technology in the constitution of physical phenomena, accordingly, no longer defined independently by matter alone, as they were in classical physics or relativity. Or so it appeared. For, quantum theory, the book further argues, made us realize that experimental technology, beginning with that of our bodies, irreducibly shapes all physical phenomena, and thus makes us rethink the relationships among matter, thought, and technology in all of physics.